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The theory of Monte Carlo modelling of distributed-parameter systems is developed from a difference-equation representation of the relevant partial differential equations. The analogy between this approach and that based on Kolmogorov's equation is used to simplify the resulting statistical model, and a number of extensions are proposed to deal with a variety of boundary types, nonlinearities, and forcing functions. The paper is completed by a series of examples illustrating the application of the extension using both digital and hybrid computers. A section is devoted to a critical assessment of the work described.